Circle Farms wants to develop a replacement policy for its 2-year-old tractor over the next 5 years. A tractor must be kept in service for at least 3 years, but must be disposed of after 5 years. The current purchase price of a tractor is $40,000 and increases by 10%

a year. The salvage value of a 1-year-old tractor is $30,000 and decreases by 10% a year.

The current annual operating cost of the tractor is $1300 but is expected to increase by 10% a year.

(a) Formulate the problem as a shortest-route problem.

(b) Develop the associated recursive equation.

(c) Determine the optimal replacement policy of the tractor over the next 5 years.